广州数学大讲坛第五期
第五十讲——北京师范大学李海刚教授学术报告
题目：Optimal Higher Derivative Estimates on Babuska Problem
时间：2024年9月11日(星期三)14：00-16：30
地点：腾讯会议（会议ID：383-997-198）
报告人：李海刚 教授
摘要：It is well known that in high-contrast elastic composite materials, the stress signifi- cantly increase in the neck region between closely spaced hard inclusions as they approach each other. This stress is represented by the gradient of a solution to the Lam\'e system. To better understand this singularity, we establish optimal higher derivative estimates for solutions to the Lam\'e system with partially infinite coefficients as the distance between the inclusions tends to zero in two and three dimensions. The sharpness of these derivative estimates is further demonstrated by a corresponding asymptotic expansion formula of the derivatives, obtained in cases where the domain exhibits certain symmetry, which includes all singular terms up to $O(1)$.
